Prime Factorization is a mathematical function utilized to break down a composite number into its prime factors. Composite numbers could be divided by more than just 1 and itself to conclude in a whole number. Prime numbers can only be divided by 1 and themselves, such as 2, 3, 5, and 7.
By finding the prime factors of a number, we can streamline fractions and equations, as well as learn the characteristics of that number. Let’s take a closer look.
Ways for Determining Prime Factorization
There are two primary processes for performing prime factorization. You could employ a factor tree, or you could factor by dividing by prime numbers. One as well as the other techniques will give you the exact outcome.
Factor Tree Method
The primary way is utilizing a factor tree. To make a factor tree:
Initiate by writing the value you are attempting to factor at the start of the page.
Below it, make branches for the factors.
Proceed by creating branches and factoring before you attain a prime number.
Here’s an example of the thinking process:
We understand that 6 * 6 = 36.
Is 6 a prime number? No. 2 * 3 = 6.
Are 2 and 3 prime numbers? Yes. We are done here.
The prime factorization of 36 would be 2 x 2 x 3 x 3. To envision this method, we could create a factor tree for 36 as follows.
As you can see, the prime factorization of 36 is found by multiplying the prime factors in the end of the tree, that is 2 * 3 * 2 * 3.
Division Method
The next way for figuring out the prime factorization of a number is to initiate utilizing a list of prime numbers. Note down the number you are attempting to factor. Then, divide the number by a prime number that divides equally into it. It’s most convenient to begin with the first few prime numbers, like 2, 3, and 5.
Let’s use the division process for prime factorization of 36.
What is a prime number that divides into 36? 2 → 2 * 18 = 36
Is 18 a prime number? No.
What is a prime number which divides into 18? 2 → 2 * 9 = 18
Is 9 a prime number? No.
What is a prime number that divides into 9? 3 → 3 * 3 = 9
Is 3 a prime number? Yes. We are done here.
The prime factorization of 36 is 2 * 2 * 3 * 3, and here’s a depiction.
Utilizing both systems, we found the prime factorization for 36 is 2 * 2 * 3 * 3.
Examples of Prime Factorization
Despite the fact that we’ve previously worked through a some examples, let’s do another one employing both methods.
Let’s utilize a factor tree to figure out the prime factorization of 100.
We learned that 4 * 25 = 100.
2 * 2 = 4, and 2 is a prime number. 5 * 5 = 25, and 5 is a prime number. We are done.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Let’s try the division process:
What is the prime factorization for 100?
What is a prime number which divides into 100? 2 * 50 = 100
Is 50 a prime number? Nope.
What is a prime number that divides into 50? 2 * 25 = 50
Is 25 a prime number? No.
What is a prime number that divides into 25? 5 * 5 = 25
Is 5 a prime number? Yes. We are done here.
The prime factorization of 100 is 2 * 2 * 5 * 5.
Applications of Prime Factorization
Prime factorization has multiple practical applications in mathematics. One of the main uses is simplifying fractions. By working out the prime factorization of the numerator and denominator of a fraction, you can cancel out common prime factors and simplify the fraction.
For instance, the fraction 8/24 could be streamlined by finding the prime factorization of both values. 8 = 2 * 2 * 2 and 24 = 2 * 2 * 2 * 3. By ruling out the common prime factor of 2, we are left with the simplified fraction of 1/3.
To see how this operates, let's utilize prime factorization to simplify the fraction 8/24. First, perform prime factorization of the numerator and denominator.
8 = 2 * 2 * 2
24 = 2 * 2 * 2 * 3
Then, we cancel out any common prime factors between the numerator and denominator.
8/24 = 2 * 2 * 2 / 2 * 2 * 2 * 3 = 1/3
After canceling out the common prime factors of 2, we are remained with the streamlined fraction of 1/3.
Prime factorization additionally plays an important role in computer science and cryptography. As you progress in advanced math and science studies, you will find further applications for prime factorization and be pleased you are an expert.
It’s Prime Time to Boost Your Math Abilities
Prime factorization is an important theory in mathematics which enables us to streamline equations and fractions, as well as learn the characteristics of a value. By practicing and comprehending the methods and utilizations of prime factorization, we can improve our mathematical skills and problem-solving abilities.
If you need assistance mastering prime factorization, contemplate contacting with Grade Potential tutoring for professional support. Grade Potential tutors are experienced and educated in math. They could provide personalized instruction and support to help you understand and utilize prime factorization in your studies.
With the help of Grade Potential tutoring, you could advance your math abilities, improve your confidence, and attain your academic goals.
